Statistics and Probability Grade 11 Quiz

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Questions and Answers

What type of random variable is 'the amount of salt in a salt solution'?

Ordinal

Discrete

Continuous (correct)

Nominal

Which of the following options indicates a discrete random variable?

Speed of a car

Amount of milk in a container

Number of consecutive tails obtained when tossing a coin (correct)

Time taken for a race

Which probability distribution shows valid probabilities for a discrete random variable?

P(1) = 0.20, P(2) = 0.30, P(3) = 0.40

P(X) = 1/10, 2/10, 4/10, 2/10, 1/10 (correct)

P(2) = 0.50, P(3) = 0.50

P(A) = 1/5, P(B) = 1/5, P(C) = 1/5, P(D) = 2/5

What is the classification for the data set P(5) = 0.11, P(10) = 0.37, P(11) = 0.52?

P Signup and view all the answers

Which of the following represents a continuous random variable?

Speed of a car Signup and view all the answers

In the context of random variables, which of the following is NOT a characteristic of a probability distribution?

It can have negative probability values Signup and view all the answers

What does the variance of a random variable measure?

The spread of the data points around the mean Signup and view all the answers

Which of these options correctly describes the mean of a given probability distribution?

It is the sum of all possible outcomes multiplied by their probabilities. Signup and view all the answers

What is the mean of the random variable X?

1.94 Signup and view all the answers

What is the variance of the random variable X?

0.64 Signup and view all the answers

How many total outcomes are there in the sample space when drawing two balls without replacement?

4 Signup and view all the answers

What is the probability of drawing exactly one blue ball when two balls are drawn?

1/2 Signup and view all the answers

What does the random variable Y represent in this situation?

Number of blue balls drawn Signup and view all the answers

What is the standard deviation of the random variable X?

0.80 Signup and view all the answers

In the context of the histogram, which value corresponds to the probability of drawing no blue balls?

1/4 Signup and view all the answers

Which of the following combinations corresponds to the outcome of drawing two blue balls?

BB Signup and view all the answers

Study Notes

Statistics and Probability Study Notes

Subject: Statistics and Probability
Year Level: Grade 11
Semester/Grading Period: 2nd Semester
Week/Session: Week 1-2

Topic: Computing the Mean, Variance & Standard Deviation of Random Variables

Problem Set 1: The problem set involves calculating the mean, variance, and standard deviation of random variables. Students must show their solutions, including given information, equations, calculation steps, and final conclusions.
Discrete vs. Continuous Variables: Test 1 asks students to identify whether a random variable is discrete (e.g., number of consecutive tails) or continuous (e.g., speed of a car).

Test I

Question: Determine if each variable is discrete (D) or continuous (C).
Examples:
- Amount of salt in a solution (C)
- Number of consecutive tails (D)
- Number of spikes scored in a competition (D)
- Speed of a car (C)
- Number of students in a school (D)

Test II

Question: Finding probability distributions for various situations.
Example: A problem involves calculating probabilities based on data given in a table.

Test 3

Question: Calculating mean, variance and standard deviation for a given data
Data type example: Number of televisions in a household.
Example: The distribution of televisions per household. The mean, variance, and standard deviation for this distribution are to be computed.

Additional Information

Additional problems: Two ball examples (red and blue) to find probability distributions by constructing a sample space, identifying outcomes and assigning probabilities. Histogram to represent probability distribution.

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Description

This quiz focuses on computing the mean, variance, and standard deviation of random variables for Grade 11 Statistics and Probability students. It also includes a section for identifying discrete and continuous variables through various examples. Students will practice problem-solving and analytical skills crucial for mastering these concepts.